
where \(B_0^c:=\mathbb {R}^N\setminus B_0\) . By the induction hypothesis and [1]}, for \(\alpha \in (0,1)\) , we have
\(\sum _{k=0}^{j-1} \int _{B_k\setminus B_{k+1}}\frac{(u(y)-m_j)^{\ell -1}}{|x_0-y|^{N+s\ell }}dy \le c \omega ^{\ell -1}R_j^{\alpha (\ell -1)-\ell s}S_\ell (\alpha ),\) 
